A tombstone is stored with the same machinery as a regular cell: a key, a deletion marker instead of a value, and a timestamp or version number. In Cassandra, for example, the timestamp is microsecond precision and last write wins, so a delete at a higher timestamp shadows any value written earlier. Reads that hit both a live value and a tombstone return nothing if the tombstone is newer.
Tombstones spread the same way data does: through replication on write, through read repair when a read finds disagreeing replicas, and through background anti-entropy processes like Merkle tree repair. The point is to give every replica a fair chance to learn about the delete before the marker is removed.
Tombstones cannot live forever or they would pile up and slow scans. Each one carries a grace period, often called gc_grace_seconds (10 days by default in Cassandra). After that window, and only after compaction runs, the database physically reclaims the space. The grace period must be longer than the time it takes for repair to reach every replica, otherwise a replica that was down could miss the delete and resurrect the row.